Question: Simplify the following expression and state the condition under which the simplification is valid: $p = \dfrac{n^2 - 4n - 5}{n^2 + 5n + 4}$
First factor the expressions in the numerator and denominator. $ \dfrac{n^2 - 4n - 5}{n^2 + 5n + 4} = \dfrac{(n - 5)(n + 1)}{(n + 4)(n + 1)} $ Notice that the term $(n + 1)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(n + 1)$ gives: $p = \dfrac{n - 5}{n + 4}$ Since we divided by $(n + 1)$, $n \neq -1$. $p = \dfrac{n - 5}{n + 4}; \space n \neq -1$